This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.
My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.
You can find my Algebra 1 (year long class) INB posts here:
And my Algebra 2 INB posts here:
And finally, my posts from a 2nd go around I’m teaching of Algebra 1 here:
The 7th priority standard we have in Algebra 1 is F.IF.8:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
I think the last three units of our Algebra 1 year tell a great story. They cycle back into each other, each one pushing a little further, and it all comes together (in the next unit!). This unit feeds off of a lot of the solution methods from the last unit, because we utilize some of these methods to rewrite a quadratic in another form.
Skill 1: I can rewrite a standard form quadratic function in a form that reveals the zeros
We begin this unit by introducing the three forms of quadratic functions and what information they can reveal to us. We won’t actually be graphing them until the next unit, but there needs to be a goal – why do we want these quadratics in different forms? So I introduced the parabola, and some of the vocabulary surrounding it.
Rewriting a standard form quadratic in factored form is pretty much the same as solving a quadratic by factoring, so I just took the chance to address some of the most common mistakes students had been making (not factoring out a GCF, misplacing negatives, getting confused by positive or negative factor pairs) and to go over the process again.
Skill 2: I can rewrite a standard form quadratic function in a form that reveals the vertex
Again, this process is fairly similar to solving a quadratic by completing the square, so I again took the chance to address some common misconceptions, and we emphasized throughout that our goal was to end up with something that looked like vertex form, so the students came up with a lot of their own ideas about what to do after they completed the square.
Skill 3: I can rewrite a factored form quadratic function in a form that reveals the y-intercept
The notes page for this is pretty basic – but I tried to emphasize as we went through it what we were actually doing. What operations are implied in the factored form function? If there’s multiplication implied, how do we multiply the two factors? What should I do with that extra coefficient?
At this point, I wanted to bring in the idea that we need to be able to 1. recognize what form a function is in by looking at it and 2. identify what form we are being asked to rewrite it in. So the last page of these notes throws in a standard form to vertex form problem, and then asks students to identify forms of some other functions and to make observations about how they can quickly identify the form (it’s all about the parentheses, right?)
It was also revealed to me that I apparently don’t know what half of 7.5 is…so just ignore all of those scribbles on that problem where I had to fix my mistake…
Skill 4: I can rewrite a vertex form quadratic function in a form that reveals the y-intercept
Something that we really focused on when looking at this skill was identifying when you were “done”. Right after you multiply out the squared binomial, it looks like you have standard form already. But, you haven’t used all of the components of the original function! So we made a point of constantly checking back in with the original function – did we use all the parts of it? If not, what parts have we not used and what should we use next in our rewriting?
Skill 5: I can rewrite a quadratic to reveal any key feature
The triangle on the front of this proved very useful as a summary of the unit – I saw students looking at it constantly as they reviewed and did their project for this unit, and I think it really helped them gain confidence that they were looking at the right set of notes and doing the right thing. I accidentally included a standard form to factored form problem that is not factorable, and although that led to a good reminder that not all quadratics are factorable, I did change it to vertex form on the file for next year.
By the end of this unit, my students for the most part felt really comfortable with the processes involved in factoring, completing the square, and multiplying out polynomials.
You can find the files for these pages here, in PDF and Publisher form.